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1D regularization inversion combining particle swarm optimization and least squares method

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Abstract

For geophysical inversion problems, deterministic inversion methods can easily fall into local optimal solutions, while stochastic optimization methods can theoretically converge to global optimal solutions. These problems have always been a concern for researchers. Among many stochastic optimization methods, particle swarm optimization (PSO) has been applied to solve geophysical inversion problems due to its simple principle and the fact that only a few parameters require adjustment. To overcome the nonuniqueness of inversion, model constraints can be added to PSO optimization. However, using fixed regularization parameters in PSO iteration is equivalent to keeping the default model constraint at a certain level, yielding an inversion result that is considerably aff ected by the model constraint. This study proposes a hybrid method that combines the regularized least squares method(RLSM) with the PSO method. The RLSM is used to improve the global optimal particle and accelerate convergence, while the adaptive regularization strategy is used to update the regularization parameters to avoid the influence of model constraints on the inversion results. Further, the inversion results of the RLSM and hybrid algorithm are compared and analyzed by considering the audio magnetotelluric synthesis and field data as examples. Experiments show that the proposed hybrid method is superior to the RLSM. Furthermore, compared with the standard PSO algorithm, the hybrid algorithm needs a broader model space but a smaller particle swarm and fewer iteration steps, thus reducing the prior conditions and the computational cost used in the inversion.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC) [grant number 41374133]. We would like to thank Editage (u]www.editage.cn) for English language editing. All authors have read and agreed to the published version of the manuscript. The work has not been published elsewhere, either completely, in part, or in another form, and the manuscript has not been submitted to another journal. During the writing process, this article was carefully reviewed and revised by the Editorial Department of Applied Geophysics and anonymous reviewers. They put forward a lot of useful comments and suggestions on this article, so we hereby express our sincere gratitude.

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Authors and Affiliations

  1. School of Geophysics and Information Technology, China University of Geosciences, Beijing, 100083, China

    Peng Su, Jin Yang & LiuYang Xu

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  1. Peng Su
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  2. Jin Yang
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  3. LiuYang Xu
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Correspondence to Jin Yang.

Additional information

Su Peng is a Ph.D. candidate majoring in geophysics at China University of Geosciences (Beijing). He graduated from China University of Geosciences (Beijing) with a master’s degree in Geodetection and Information Technology in 2019. His main research interests are geophysical electromagnetic forward and inversion.

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Su, P., Yang, J. & Xu, L. 1D regularization inversion combining particle swarm optimization and least squares method. Appl. Geophys. 20, 77–87 (2023). https://doi.org/10.1007/s11770-022-0950-6

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